>>>>>==============>
We have added two new videos to our Chance Lecture Series.

The
first video is of a talk that Freeman Dyson gave in a 1994
Dartmouth Chance course. Dyson discusses several chance issues
that he has dealt with in his long scientific career. He begins
with his early days as a statistician when, in the second world
war, he was asked to determine if experienced bombers had a better
chance of returning than did inexperienced bombers. They did not
but for a surprising reason. He next discusses problems in
determining if electromagnetic fields cause cancer clusters. He
then discusses the risk of asteroids hitting the earth and how we
should respond to this risk. Finally, on the lighter side, he
gives his thoughts about Richard Gott's method of determining
confidence limits for the length of life on earth, the maximum
population, the length of this Chance News, etc.(See Chance News
2.11,
2.12,
2.13,
2.14.)

The
second video is a lecture entitled "Probability and DNA" given
by Jonathan Koehler this summer at the Dartmouth Business School.
Koehler begins with a discussion of intuition in probability and
how it differs from intuition in other fields. He carries out
experiments based on simple Bayesian examples to show how our
intuition can lead us astray. He discusses the problems people
have with conjunction and disjunction of events. Of course, he
cannot resist including the infamous Linda problem. Koehler
describes experiments with jurors that show that lack of
understanding of how to combine probabilistic information can
cause jurors serious problems. In particular, he describes
experiments that show that about 50% of jurors would vote to
convict in a DNA trial when told that the chance of an innocent
person matching the DNA was 1 in a million, and this proportion is
not significantly changed when jury members are given the
additional information that there is a 2% chance of a lab error.
Koehler ends with an interesting discussion of the role of
probability in the legal concept of "beyond a reasonable doubt". A
lively and informal talk backed up with lots of data.

<<<========<<

>>>>>==============>
This Fall David Howell, in the Psychology Department at the
University of Vermont, is teaching the third version of his Chance
type course: Psychology 95: Lies, Damn Lies, and Statistics.
Howell is experimenting this year with making the course much less
dependent on in-class lectures and activities and more on students
working with each other and himself using electronic sources. The
entire course will evolve on the web and you can follow it at:
Psychology 95

Howell's course is the first serious use of our Chance videos,
that we have heard about. We would appreciate hearing from others
who have used one or more of the videos, successfully or
unsuccessfully.

<<<========<<

>>>>>==============>
John Pezzullo at Georgetown University told us about
his web site
that provides links
to web pages that perform statistical calculations. There are also
links to online statistics books, tutorials, and related
resources. Pezzullo's web site is well organized and up-to-date.
It has over 260 links and growing!
<<<========<<

>>>>>==============>
We are trying to decide how useful it is to provide links to NPR
programs that discuss Chance News items that are also reported in
newspapers. To help us with this, we would like to suggest that
some of you try an experiment with your students to assess the
value of the two different media.

A study that would be good to use for such an experiment is the
recent study carried out at Carnegie Mellon University suggesting
that people who use the internet are more subject to depression
than those who do not. This study was discussed on NPR on Talk of
the Nation 4 Sept. 1998. You can
listen to this.

You might ask your students to listen to the NPR program and read
one of the newspaper articles and ask them which media they
preferred and which they felt explained the study the best. It
might be interesting to include a comparison of the two newspaper
articles. Another possibility would be to divide the class into
three groups and have different groups use different sources.
Perhaps you or your class can come up with another relevant
experiment. If you try any such experiment, please pass the
results on to us and we will report what we learned in the next
Chance News. To not muddy the waters, we will not give our own
review of this study.

<<<========<<

>>>>>==============>
Ken Steele wrote to us about the following graphics problem:
National Geographic, August 1998
Letters to the editor

A graph in an article on global warming in the May 1998 issue of
the National Geographic gave the projected temperatures in the
Southeast U.S. for July 1 during the years from 2000 to 2500. The
caption states:

Given an expected doubling of CO2 by 2100, July
temperatures in the Southeast U.S. would approach
100 F, a 20 percent increase over today's (about 83 F).

A letter to the editor states:

In the caption for the graph titled "Steamy
Summers for Southeast U.S." (page 69), you state
that a temperature increase from about 83 F to
100 F is a twenty percent increase. This is
incorrect. If a temperature change is to be
expressed as a percentage change, a scale such
as Kelvin--for which zero is the lowest temperature
possible--should be used. In this case the temperature
change is from 302K to 311K, an increase of 3 percent.

Anton Sawatzky
Pinawa Mannitoba

DISCUSSION QUESTIONS:

(1) Isn't it true that the temperature expressed in Fahrenheit
will have increased by twenty percent if the projections are
correct? Do you agree with the reader that this statement is
incorrect? Why?

(2) In response to the letter the editor writes:

We regret the error and also our use of an
inaccurate label in the illustration. The
graph does not represent temperature alone,
as indicated, but rather heat index. This
is a measure of how warm it feels, based on
a combination of humidity and temperature.

Does this change anything?

<<<========<<

>>>>>==============>
Peter Doyle raised an interesting question related to a well known
example that Kahneman and Tversky used to illustrate what they
call "representatives". (Peter found this example discussed in a
new book "The Mind's Past" by our colleague Michael Gazzaniga).
Here is the problem as stated in Kahneman and Tversky's article:
Subjective Probability: a Judgment of Representiveness, Cognitive
Psychology, 3 (1972), 430-454:

All families with six children were surveyed in a city.
In seventy-two families the exact order of births of boys
and girls was GBGBBG.
What is your estimate of the number of families surveyed
in which the exact order of births was BGBBBB?

The authors write:

The two sequences are about equally likely, but most
people will surely agree that they are not equally
representative. The sequence with five boys and
one girl fails to reflect the proportion of boys
and girls in the population. Indeed, 75 of 92
subjects judged this sequence to be less likely
than the standard one.

Peter asks: What distribution should we expect for birth orders
for families with six children? Surely not a uniform
distribution! We do not know the answer but are trying to get the
data to answer his question. We would appreciate hearing from
anyone who knows a source for the relevant data.

The data for gender order in families with two-children was
provided by Will Lassek in a letter to Marilyn vos Savant (See
Chance News 6.12.) From his data it is clear that a person asked
to compare the frequency of BG and GG in families with two
children would be quite justified in estimating fewer GG families.
See discussion question (2).

DISCUSSION QUESTIONS:

(1) Here is a favorite discussion question in a Chance class:
Assume that gender of offspring can be considered like coin
tossing. If families have children until they have a boy or until
they decide not to have more children would there be more boys or
girls. The answer is the same.

Under these assumptions what proportion of the families with six
children would you expect to have gender order GGGGGB and what
proportion to have gender order BGBBBB?

(2) Thanks to reader Will Lassek of Marylin vos Savant's column
(see Chance News 6.12), we have the data to look at the
distribution of two-children families. Lassek says that he looked
at the gender order for the 42,888 two children families in the
342,018 families included in the National Interview Survey carried
out by the census bureau from 1987 to 1993. (We assume this means
the National Health Interview Survey.)

It is generally assumed that there are about 105 boys born for
each 100 girls. Assuming a Bernoulli process with probability of
a boy = 105/205 = .512 and a girl = .488 we found:

This gives a chi^2 value of 64.9753 and so the chi^2 test would
certainly reject this Bernoulli model.

Can you explain why this model does not fit?

<<<========<<

>>>>>==============>
Here is an article that suggests that the distribution of birth
order in families of a given size could change considerably in the
future.
Researchers report success in method to pick baby's sex
The New York Times, 9 Sept. 1998, A1
Gina Kolata

The Genetics & IVF Institute in Fairfax VA. has developed a method
to allow a couple to have a good chance of having a child of a sex
it chooses. The method uses the fact that the only difference
between sperm that carry the Y chromosome, which produces males,
and sperm that carry the X chromosome, which produces females, is
that the sperm with the Y chromosome have about 2.8 percent less
genetic material.

The process lines up the sperm individually in a stream and
measures the DNA content for each sperm. Sperm containing the X-
chromosome are separated from those with a Y chromosome. It takes
about a day to sort the 200 million sperm of a single ejaculate.
The sperm are then used for artificial insemination.

In a paper
being published in the current issue of the journal
Human Reproduction, the
investigators report results for couples who wanted girls. Ten
out of 11 babies born so far were girls.

The researches have carried out a similar number of pregnancies
where boys are desired, but this article states that the
researchers are not releasing the results until they are
published. However, from the
Institute's home page we find that the company
estimates that the procedure makes it 5 or 6 times more likely to
have a girl for those wishing a girl and about 2 times more likely
to have a boy than girl for those who prefer a boy.

Couples with a family history of sex-linked diseases (illnesses
that are genetically tied to either the X chromosome or the Y
chromosome, such as hemophilia) could use sperm-sorting to avoid
the chromosome that carries the disease.

But the institute has found that most couples who want to select
the sex of their children do so for reasons of "family balancing".
For example, a couple may already have three children, all of whom
are boys, and want the fourth to be a girl. The institute offers
the sex determination option to such couples. It does not offer
the procedure to couples without children who want a particular
sex. However, a spokesman said that this policy could change.

DISCUSSION QUESTIONS:

(1) Do you see any ethical problems with allowing families to
choose the sex of their children?

(2) What do you think will happen to the gender distribution of
single and two child families if it becomes really easy for
families to choose the sex of their children?

This article on coincidences is excerpted from an article by
Martin in the Sept-Oct issue of Skeptical Inquirer. Of course,
the article starts with the infamous birthday problem and the well
know examples of "unbelievable" coincidences such as the numerous
similarities between Lincoln and Kennedy: both assassinated on
Friday, both succeeding vice presidents were southern Democrats
and former senators named Johnson with 13 letters in their names
and born 100 years apart etc.

Martin then remarks: so far as is known, the decimal digits of the
irrational number pi are random. He then goes on to say that
since the digits are random we can model coin-tossing using the
expansion for pi (H = even digit, T = odd digit). He then shows
that he can find streaks and other unusual sequences by fishing
around in this random sequence. This is supposed to show that the
coincidences in our life are really just chance events that are
selected out of a huge set of things that happen to us.

The article in the Skeptical Inquirer discusses these examples
plus a discussion of random prices in the stock market. Again
Martin uses the digits in the expansion of pi to generate stock
prices and then shows that he can find in these random prices
behavior that technical market analysis consider peculiar to the
stock market.

In the original article an insert (presumably by the Skeptical
Inquirer) remarks:

Back in 1992, the Skeptical Inquirer held a Spooky
Presidential Coincidences Contest, in response to
Ann Landers printing "for the zillionth time" a list
of chilling parallels between John F. Kennedy and
Abraham Lincoln. The task was for readers to come
up with their own list of coincidences. The results
were impressive and can be found in Skeptical
Inquirer Spring 1992, 16(3), and Winter 1993,17(2).

DISCUSSION QUESTIONS:

(1) Martin states that the digits of pi being random means that
the value of any single digit is not predictable from preceding
digits. What does this mean?

(2) Do you think that the pi example would convince your Uncle
Joe that there was nothing strange about getting a call from his
college roommate Peter, who he had not heard from for 30 years,
the day after he dreamed about him?

From the top of Mt. Washington the Weather Notebook presents the
following problem:

What are the chances that you have breathed the same air as
Copernicus?

This is an old problem. Warren Weaver, in his book Lady Luck
attributes it to Sir. James Jeans who asked for the probability
that a breath you take includes molecules from Julius Caesar's
last breath. However, if you want to make your own calculations
you can find how to enter the contest at the url given above.

<<<========<<

>>>>>==============>
Joan Garfield suggested that we include the NPR program dealing
with the salt controversy. She was impressed that one of the
speakers used the central limit theorem in his argument.
NPR: The Talk of the Nation, 14 Aug. 1998
Global Warming; News/diet and blood pressure

The two topics discussed in this hour, global warming and
recommendations on salt, illustrate the difficulty in getting
scientists to come to an agreement on how to interpret scientific
studies. We will consider only the salt controversy. The most
complete article in the current news on this topic is:

This is a long article that provides a case study of a national
health recommendation: eat less salt. For three decades the
National Heart, Lung and Blood Institute, and the National High
Blood Pressure Education Program and numerous other organizations
have recommended a daily allowance of 6 grams of salt. This is
based on the theory that lowering salt intake will lower blood
pressure and prevent strokes.

The original recommendation was based on "ecological" studies that
showed that countries whose population had low salt diets had
lower rates of hypertension. Unfortunately, studies within a given
population did not show that those with low salt diets had lower
blood pressure than those with high salt diets. By now there have
been many more studies including controlled studies. However,
researchers took their position on this issue before there were
many studies and seem to be able to interpret modern studies to
fit their position. This has kept scientists divided and makes it
impossible to reach a consensus on the proper role of salt in our
diet.

Taubes writes:

While the government has been denouncing salt as a
health hazard for decades, no amount of scientific
effort has been able to dispense with the suspicions
that it is not. Indeed, the controversy over the
benefits, if any, of salt reduction now constitutes
one of the longest running, most vitriolic, and
surreal disputes in all of medicine.

Taubes also states:

The controversy itself remains potent because even a
small benefit--one clinically meaningless to any single
patient--might have a major public health impact. This
is a principal tenet of public health: Small effects
can have important consequences over entire populations.

Richard Peto has stated that, if by eating less salt the world's
average blood pressure could be reduced by a single millimeter of
mercury, that would prevent several hundred thousand deaths a
year. The problem is that small effects are very difficult to
establish by statistical studies. Recent studies have suggested
that too little salt may cause other problems. If so it might
make more sense to limit salt only for those who have high blood
pressure.

The use of the Central Limit Theorem in the NPR discussion arose
over such a point. One expert argued that too little salt meant
less than the 6 grams a day recommended so would not occur if
people followed the recommendation. The other expert then pointed
out that, if the present recommendations were followed, you would
have a normal distribution with mean 6 and could expect
significantly lower levels for a reasonable proportion of the
population.

DISCUSSION QUESTION:

How can an effect be clinically meaningless for any single patient
but yet save hundreds of thousand lives?

A three-judge Federal panel, in a lawsuit filed by the House of
Representatives against the Commerce Department, ruled that plans
to use sampling in the 2000 census violated Federal laws. The
first article gives excerpts from the ruling that indicated the
courts reasoning.

Since the Constitution specifies enumeration, the court felt that
the claim that statistical sampling in the apportionment
enumeration does not violate the Census Act must come from the
1976 amendments to sections 141(a) and 195 which addressed the
problem of sampling.

The post-1976 version of sections 141(a) states:

The Secretary shall, in the year 1980 and every
10 years thereafter, take a decennial census of
population...in such form and content as he may
determine, including the use of sampling procedures
and special surveys.

The 1976 amendment to section 195 more specifically states:

Except for the determination of population for
purposes of apportionment of Representatives in
Congress among the Sates, the Secretary shall,
if he consider it feasible, authorize the use of
statistical method known as "sampling" in carrying
out the provisions of this title...

The court ruled that these amendments should be considered
together when deciding on sampling. Thus it was argued that the
case rests on whether the exception stated in the amendment to
section 195 meant "you cannot use sampling methods for purposes of
apportionment" or "you don't have to use sampling methods". To
settle this use of English the court provided the following two
examples of the use of the word except:

Except for Mary, all children at the party shall
be served cake.
Except for my grandmother's wedding dress, you
shall take the contents of my closet to the cleaners.

The court argues that the interpretation of except must be made in
the context of the situation. In the first example, it would be
all right if Mary were also served cake. In the second example,
it would not be all right if grandmother's delicate wedding dress
were sent to the cleaners. It is argued that the context of the
census is similar to the second example and so the exception means
that you really cannot use sampling for apportionment purposes.

The Clinton government is appealing this ruling to the Supreme
Court and the Supreme Court has agreed to accept the appeal and
put it on the fast track so that a decision could come by March.
Commentators on the NPR program point out that, in fact, the
Congress has the last say on this issue.

There were lots of interesting letters to the editor on this
issue. Here is our favorite:

To the Editor:
Republicans claim that sampling cannot be used in the census
because it violates the constitutional requirement of an
"actual enumeration", interpreted to mean a literal head
count (editorial, Aug. 25).
There are ways to count other than adding 1 many times. For
instance, multiplying the two sides of a checkerboard (eight
squares each) would yield a total of 64 squares, whereas a
hand count might yield 63 or 65 because of human error.
Human intelligence plus a little brute force is often far
more efficient and accurate than brute force alone. This
is why statistical sampling is the superior way to carry
out an "actual enumeration" of a large population. Just
ask any Republican who relies on a poll or who takes a
blood test rather than drain every drop from his body.
BRIAN CONRAD
Cambridge, Mass., Aug. 25, 1998

The writer is an assistant professor of mathematics at Harvard
University.

The article by Weinstein is the only one we saw that pointed out
that statisticians themselves are not in agreement about the
sampling methods the census bureau plans to use. He writes:

The handful of statisticians who have mastered the
ferocious mathematical and practical complexities
are split over the usefulness of sampling. William
Kruskal, former chairman of the Statistics department
at the University of Chicago, speaks for many of his
colleagues when he admits that "no one really knows".

Weinstein makes clear that this statement is in reference to
sampling methods relating to the undercount problem and goes on to
state that most experts do agree that the use of sampling to
complete the census, after getting responses from 90% of the
households is a sensible way to cut the soaring costs of
conducting the census without sacrificing accuracy.

In his article, Weinstein makes a valiant effort to explain the
concerns that some of the statisticians have about the sampling
methods proposed for the undercount problem. However, these are
difficult ideas and if you really want to understand what the
issues are, you will be better off reading the following paper by
David Freedman and his colleagues.

Planning for the census in the year 2000Technical report No. 484,
Department of Statistics, U.C. Berkeley
David Freedman et al.

A more up-to-date version will be also available soon. We will
give the reference in the next Chance News. While you are getting
the census article we strongly recommend that you also get David's
most recent paper: "From Association to Causation: some remarks on
the history of statistics", Technical Report No. 521, August 1998.
Here you will find Freedman's thoughts on this classic problem in
the context of his discussion of famous experiments such as John
Snow's demonstration that cholera is a waterborne infectious
disease, and studies identifying the health hazards of smoking.

We remind readers that the discussion of the technical problems
involved in the undercount question from the point of view of the
Census people can be found in Tommy Wright's article in the May-
June 1998 issue of the American Scientist (See Chance News 7.06)
and in
his presentation in our Chance Lectures Series.

In the second half of the NPR program there is a discussion of the
need for scientists to explain the issues involved using sampling
for the undercount problem in such a way that the public and
congressmen can understand them. Shortly after this discussion,
Fienberg is invited to explain the undercount method in terms of
estimating the number of fish in a lake. Have your students
listen to this and see if they get it.

DISCUSSION QUESTIONS:

(1) One letter to the editor went something like this: The next
thing you know they will be proposing that we elect our President
by the results of a poll. What do you think of this argument?

(2) What do you think about the courts' linguistic argument?

(4) The NPR program opens with the remark: The 1990 count missed
almost 2% of the population. This meant that more than 8 million
people were not counted. A listener called in and said he did not
see how this could be unless the population of the U.S. had
suddenly increased to 400 million. Steven Fienberg offered an
explanation -- could you?

<<<========<<

>>>>>==============>
Dan Rockmore heard on NPR a discussion of the relation between
investment and gambling by the Motley Fools. It turned out that
this was one of their earlier essays and Dan found it on the
Motley web site.
Foolish gamblingThe Motley Fool, 3 April 1997
Mark Brady

Brady states that the boundaries between investing and gambling
are getting blurred. He remarks that the state government blurs
it by trying to drag investing down to the level of gambling. He
cites the ad:

Saving for a rainy day takes too long; you could win $50,000
instantly if you play the lottery.

As another example, he cites the discussion about changing social
security to make it based on the stock market rather than Treasury
Bonds. On the other hand, financial service people want to take
advantage of the popularity of lotteries to sell their services.

Brady also discusses the innumeracy of the public and gives some
examples. For his first example he says:

Innumerate people will prefer a 10% raise in a period of
15% inflation over a 5% raise in a period of 3% inflation.

For his second example he writes:

Most people cannot do the odds. What is a better deal
over a year? A 100% safe return with 5% interest or a
90% safe return with a 20% return. For the first deal,
your return will be 5%. For the second, your return will
be 8%.

He closes with the comment:

Remember that, buried beneath all the talk of betting, risk and
odds, are two simple numbers that the state does not want you to
think about. The lottery returns 50 cents on the dollar while the
stock market returns 110 cents. Any Fool can see which is the
best.

DISCUSSION QUESTIONS:

(1) In Brady's inflation argument, what is the real choice you
are offered? Dana Williams remarks that he would certainly choose
the 5% just to get the 3% inflation.

(2) Brady gets his 8% return for the 90% save return with a 20%
return by asking you to consider investing $1000 10 times and to
assume that 9 of the 10 times you win. Then you made $1800 and
lost $1000 for a net return of $800 or 8% on your $10,000
investment. But does this answer the original question related to
a single choice?

(3) Do you agree that the stock market returns 110 cents on a
dollar?

<<<========<<

>>>>>==============>
The next article was suggested by Elizabeth Walters.

When you read the article you find that the variable lurking in
the background is lack of sleep.

The article states that the connection between tonsils and
children's abilities has long been known. An example of this is a
study reported in 1889 in the British Medical Journal titled "The
awkwardness and stupidity of children with large tonsils."

A study by Dr. David Gozal in the September issue of Pediatrics
purports to explain this by showing that the real problem is sleep
apnea which causes children to wake up many times during the night
and leaves them feeling tired the next day. According to Gozal,
sleep apnea can often be cured by removing the tonsils and
adenoids. This, in turn, improves the student's grades.

For this study Gozal questioned the parents of 300 first-graders
whose school performance was in the bottom tenth of their class.
Symptoms of sleep apnea were found in 54 children. Parents of
these children were advised to consult their doctors to consider
having their children's tonsils and adenoids removed. The parents
of 24 of these 54 children decided to have this done and 30
decided not to. The article says that, a year later, almost all
the children who underwent surgery had improved their school
performance an average of half a letter. The grades of the
students who remained untreated remained the same. We found this a
little confusing and so consulted the original to see what it
meant.

In the original article the grade improvement is described as
follows:

Grades were on a scale 0 to 4 with 2 a minimal passing grade and 2
to 2.5 representing poor performance.

For the 24 treated, the mean grade in first grade before treatment
was 2.42 with sd .17 and in the second grade after treatment it
rose to 2.87 with sd 19.

For the 30 not treated, the mean grade in first grade was 2.44
with sd 13 and in the second grade 2.46 with sd 15.

All those treated improved their scores from first to second grade
although 2 were still in the lowest 10th percentile of their
class.

DISCUSSION QUESTIONS:

(1) Do you find this a definitive study? What other questions
would you like to have answered about the study to evaluate it?

(2) Is it true that almost all of those treated raised their score
by an average of half a letter? How many would you estimate the
number who did raise their grade by 1/2 a letter?

This article describes three mechanical processes for estimating
e, gives the underlying theoretical justifications, and presents
the results of computer simulations of the physical experiments.

One method uses derangements, permutations leaving no element in
its original place: randomly permuting 10 elements 10^5 times,
it uses the reciprocal of the proportion of outcomes yielding
derangements as an estimate of e.

A second method tosses 10^5 darts at a board consisting of 10^5
equally likely target regions; by the binomial model and/or the
Poisson approximation thereto, the ratio of 10^5 to the number of
regions with no hits approximates e.

The last method involves shaking N salt particles at random onto
a table with area A having a hole with area a on it. Then p = a/n
is the probability that any one particle goes through the hole.
After the shaking there will be a number N1 that did not go
through the hole. These N1 particles are again shaken onto the
table with a resulting N2 not going through the hole. This
process is interated n times. Since each of the N particles has
probability (1-1/p)^n of having not gone through the hole the
expected value of Nn = N*(1-p)^n. If we choose n = 1/p, then Nn/N
becomes an estimate for 1/e. For his experiments the author used N
= 50,000. He chooses the area of the hole and the table so that p
= 1/10,000 and e is estimated as N/Nn. This whole process is
repeated 100 times resulting in 100 estimates for e.

The first two methods were simulated 1,000 times, the third one
was repeated only 100 times. Results of simulations suggest
that the second (dart board) method uses the fewest computer
resources for a given level of accuracy and precision:

The author explains the differences in accuracy, precision, and
relative effort among the three methods as follows:

The dart method involves only one parameter, i.e, the
number of darts, N, which needs to be chosen very large
to guarantee a reasonable estimate of e. The derangement
method, on the other hand, involves two parameters, i.e.,
the number of objects in the array, N, and the number of
permutations or shufflings. The former needs to be only
moderately large (ten in our simulation), but the latter
has to be very large to ensure sufficient convergence.
This causes the derangement method to be less efficient
than the dart method. Finally, the salt-shaker algorithm
involves two parameters, i.e., the number of particles, N,
and the number of iterations, n, both of which have to be
very large. This causes the computations to be exceedingly
slow and, consequently, renders the algorithm very
inefficient. Finally, the salt-shaker algorithm involves two
parameters, i.e., the number of particles, N, and the number
of iterations n, both of which have to be very large. This
causes the computations to be exceedingly slow and,
consequently, renders the algorithm very inefficient.

DISCUSSION QUESTIONS:

(1) What is the distinction between slowness of computations and
inefficiency of an algorithm? If they are distinct, why does the
former imply the latter?

(2) Do the numbers of parameters really explain the differing
effectiveness of the methods here, or are the choices of numbers
of iterations, regions on a dartboard, elements permuted, etc.
more fundamental?

(3) Readers may find it interesting to consider how one could
estimate, in advance of the simulations, measures of their
effectiveness. There is room for further study here.

The article opens with the assertion that, since the 1970s,
virtually all income gains in the US have gone to households in
the top 20% of the income distribution. This is the greatest
inequality observed in any of the world's wealthy nations, a fact
largely ignored in the current rosy picture of corporate
profitability, widespread job creation and negligible inflation
(note that the article appeared before our stock market meltdown
of recent weeks!).

While previous writers have expressed moral concerns with the
growing income inequality, there is now evidence of a medical
downside as well. Research indicates that countries with more
pronounced differences in incomes experience shorter life
expectancies and greater risks of chronic illness. The risks are
described as being as large in magnitude as those linked to more
widely publicized factors, such as cigarettes or fatty foods.

As a historical perspective, the article cites a 20-year-old study
of 17,000 British civil servants which found that the annual heart
attack fatality rate was four times as high among clerks and
messengers as for administrators, despite the fact that the clerks
could afford reasonable housing and had access to national health
care. Moreover, the effect persisted even among workers at the
high end of the income distribution; for example, a senior
statistician had twice the risk as did a chief statistician. This
led Michael Marmot, a University of London epidemiologist, to
conclude that factors beyond class-related differences in diet and
smoking were involved. He suggested that job control and sense of
security also played a role.

Richard Wilkinson, an economic historian at Sussex University took
the analysis one step further, looking at health differences among
different countries. He found that, among nations with gross
domestic product at least $5000 per capita, one nation could have
twice the per capita income of another yet still have a lower life
expectancy. On the other hand, income equality emerged as a
reliable predictor of health. The finding ties together a variety
of international comparisons. For example, the greatest gains in
British civilian life expectancy came during WWI and WWII, periods
characterized by compression of incomes. By contrast, over the
last ten years in Eastern Europe and the former Soviet Union,
small segments of the population have had tremendous income gains
while living conditions for most people have deteriorated. These
countries have actually experienced decreases in life expectancy.
Among developed nations, the US and Britain today have the largest
income disparities and the lowest life expectancies. Japan has a
3.6 year edge over the US in life expectancy (79.8 years vs 76.2
years) even though it has a lower rate of spending on health care.
The difference is roughly equal to the gain the US would
experience if heart disease were eliminated as a cause of death!

The July 1998 issue of the "American Journal of Public Health"
presents analogous data in comparisons of US states, cities and
counties. Research directed by John Lynch and George Kaplan of the
University of Michigan finds that mortality rates are more closely
associated with measures of relative, rather than absolute,
income. Thus the cities Bixoli, Mississippi, Las Cruces, New
Mexico and Steubenville, Ohio have both high inequality and high
mortality. By contrast, Allentown, Pennsylvania, Pittsfield
Massachusetts and Milwaukee, Wisconsin share low inequality and
low mortality.

DISCUSSION QUESTION:

It is easy to see how to compare mortality rates among
communities. How do you think "income inequality" is measured?

<<<========<<

>>>>>==============>
Driving while black; a statistician proves that prejudice still
rules the road
The Washington Post, 16 August 1998, C1
John Lamberth

Lamberth is a member of the psychology department of Temple
University. In 1993, he was contacted by attorneys whose African-
American clients had been arrested on the New Jersey Turnpike for
possession of drugs. It turned out that 25 blacks had been
arrested over a three-year period on the same portion of the
turnpike, but not a single white. The attorneys wanted a
statistician's opinion of the trend. Lamberth was a good choice.
Over 25 years his research on decision-making had led him to
consider issues including jury selection and composition, and
application of the death penalty. He was aware that blacks were
underrepresented on juries and sentenced to death at greater rates
than whites.

In the article, he describes the process of designing a study to
investigate this question. He focused on four sites between Exits
1 and 3 of the Turnpike, covering one of the busiest segments of
highway in the country.

The first challenge was to define the "population" of the highway,
so he could determine how many people traveling the turnpike in a
given time period were black. Lamberth notes that Census data
don't exist for this question. He devised two surveys, one
stationary and one "rolling." For the first, observers were
located on the side of the road. Their job was to count the
number of cars and the race of their occupants during randomly
selected 3-hour blocks of time over a two-week period. During 21
recording sessions. from, June 11 to June 24, 1993, his team
conducted over 20 sessions, counting some 43,000 cars, 13.5% of
which had one of more black occupants. For the "rolling survey",
a public defender drove at a constant 60 mph (5 mph over the speed
limit), counting cars that passed him as violators and cars that
he passed as non-violators, noting the race of the drivers. In
all, 2096 cars were counted, 98% of which were speeding and
therefore subject to being stopped by police. Black drivers made
up 15% of these violators.

Lamberth then obtained data from the New Jersey State Police and
learned that 35% of drivers stopped on this part of the turnpike
were black. He says "in stark numbers, blacks were 4.85 times as
likely to be stopped as were others." He did not obtain data on
race of drivers searched after being stopped. However, over a
three year period, 73.2% of those arrested along the turnpike by
troopers from the area's Moorestown barracks were black, "making
them 16.5 times more likely to be arrested than others."

Lamberth's finding that blacks were being stopped at rates
disproportionate both to their numbers on the road and their
tendency to speed led to a March 1996 ruling by New Jersey
Superior Court. Judge Robert E. Francis ruled that state police
were effectively targeting blacks, violating their constitutional
rights. Evidence gathered in the stops was suppressed.

Lamberth speculates that drug policy is the reason for police
behavior in these situations. Testimony in the Superior Court
case revealed the troopers' performance is considered deficient if
they do not make enough arrests. Police training targets
minorities as likely drug dealers, and in this sense the officers
had an incentive to stop black drivers. But when Lamberth
obtained data from Maryland (similar data has not been available
from other states) he found that about 28% of drivers searched in
that state have contraband, regardless of race. Why then, the
perception that blacks are more likely to carry drugs? It turns
out that, of 1000 searches in Maryland, 200 blacks were arrested
compared to only 80 non-blacks. More blacks being arrested for
drugs feeds the perception that they are the principal
perpetrators. The problem is that the sample is biased: of those
searched, 713 were black and 287 were non-black.

DISCUSSION QUESTIONS:

(1) How did Lamberth arrive at the figure that blacks were 4.85
times as likely to be stopped as others? What about the figure
that blacks were 16.5 times more likely to be arrested?

(2) How do the data in the last paragraph show that the chance
that a search will produce drugs does not depend on race?

In her column on May 31 of this year (discussed in Chance News
7.06), Marilyn gave a curious explanation of the margin of error
for an opinion poll. Her conclusion was that "the published
margin of error on a poll merely tells us the size of the sample."
This provoked the following response from Kathleen Frankovic,
writing on behalf of the American Association for Public Opinion
Research: "Your answer about the source of a poll's margin of
error was incomplete. When conducting a poll, we can calculate
the error that comes from selecting a sample, if that sample is
representative of all people. 'Margin of error...' refers to the
sampling error."

Marilyn agrees with Frankovic's description but maintains that her
original comments were correct. The guiding principle, she says,
is that, the larger the sample the more accurate the poll. "So,
if a poll is conducted properly, the published margin of error--
while it literally refers to all sampling errors--is more an
indicator of the size of the sample than anything else."

Pollsters also objected to her comment that the margin of error is
based on past polls. Here she amplifies that comment, explaining
that she meant that the formulae applied to present polls are
derived from experience with past polls.

DISCUSSION QUESTIONS:

(1) Does Marilyn understand the difference between accuracy and
precision?

(2) What do you think she means by the phrase "while it literally
refers to all sampling errors"?

(3) Do you agree that the margin of error is based on experience?

-----------

Also in the present column, Marilyn responds to an anonymous
reader who asked Marilyn to settle a dispute about whether a
child's IQ can never be higher than his parents' IQs. Marilyn
says that the child's IQ can indeed exceed his parents' but adds
that the reader may be thinking of an effect known to
statisticians as regression to the mean. In lay terms, she
describes this as meaning that "within a given population, average
intelligence appears stable, but people tend to be more average
than exceptional." She asserts that, if both parents have IQs of
125, they are more likely to have a child with an IQ in the range
100-125 than an IQ exceeding 125.

DISCUSSION QUESTIONS:

(1) Comment on Marilyn's description of regression to the mean.

(2) Do you agree with her probability assessment? What
assumptions are you making?

According to John Manning, an evolutionary biologist at the
University of Liverpool, comparing the length of the fingers on a
man's right hand with his left gives an indication of his
fertility: less match between the fingers indicates fewer and
less active sperm. Further information is available from the
relative lengths of fingers on the same hand: men whose ring
fingers are much longer than their index fingers tend to have
higher levels of the male hormone testosterone. Although the
claims may seem outrageous, it was biological evidence led Manning
to consider the link. Experiments in mice showed that the same
set of genes that control development of fingers and toes also
control the ovaries and testes.

Manning reports running three separate tests. The first involved
100 men and women at a fertility clinic, the second involved 10
healthy men; and the third looked at 300 men and women who have
children. Sometimes he tested fertility by measuring sperm or
hormone levels, while other times he tried to gauge it after the
fact by the size of the subject's families. But he says the link
with finger size always showed up. His results were announced in
"New Scientist", and he claims they have been accepted for
publication in two scientific journals.

Reaction from the medical community is mixed. Doctors quoted in
the article urged caution in interpreting the results and called
for further review of the study. Dr. Merle Berger of Beth Israel
Deaconess Medical says he is "dumbfounded by the whole thing
because it's so complicated. If there were some truth to this it
would be very subtle differences in length that would have to be
accurately measured. It would not be just the way it looked."

The Globe article, meanwhile, closes on an even more skeptical
note. It quotes a palm reader who says she too can tell people
how many children they will have by looking at their hands!

DISCUSSION QUESTIONS:

(1) What problems do you see with Manning's samples? What about
his definition(s) of fertility?

(2) How do you reconcile the headline of the article with the
tone of the closing?

<<<========<<

>>>>>==============>
In mammogram debate, a new guide
The Boston Globe, 29 August 1998, A3.
Richard Saltus

In past editions of Chance News, we have reviewed numerous
conflicting reports on whether mammograms are beneficial for women
in their 40s. Overall this age group has a relatively low risk
for breast cancer, but the risk rises quickly with age. On the
other hand, it has not been clear how to balance this concern with
the high false positive rate reported for screening in this age
group.

Now scientists at the National Cancer Institute have developed a
formula to help women calculate whether their personal risk is
high enough to justify having an annual mammogram. Writing in the
"Journal of Clinical Oncology", Dr. Mitchell Gail and
biostatistician Barbara Rimer explain that the method is designed
to identify women in their 40s who, because of family history or
other risk factors, have a least as great a chance of developing
cancer as a woman in her 50s with no risk factors.

The paper describes two versions of the method, an "exact age"
procedure and a "grouped age" procedure that uses two ages, the
groups 40-44 and 45-49. In either case, women begin with a
checklist of what are called "strong" risk factors: previous
breast cancer; the BRCA1 or BRCA2 genes; a mother, sister or
daughter with a history of breast cancer; abnormal cells found in
a previous biopsy; 75% or more dense breast tissue at age 45-49;
and two or more previous biopsies. A woman with none of these
conditions then checks a table of weaker factors: age at
menarche, number (0 or 1) of previous biopsies and age at which
she first gave birth. Values from these factors are combined with
the woman's age to compare her risk of developing cancer in the
next year to the risk for a 50-year-old woman with no risk
factors.

DISCUSSION QUESTION:

(1) What do you see as the advantages of having such a formula?
Do you see any downside?

(2) Dr. Mary Burton, a physician affiliated with the Harvard
Vanguard Medical Associates, is quoted as saying: "Any method that
helps clarify clinical risk to patients will help patients make
better decision for themselves." Do you agree?

<<<========<<

>>>>>==============>
S.A.T. scores decline even as grades rise
The New York Times, 2 September 1998, B8
William H. Honan

This year, 38% of S.A.T. test-takers had 'A' averages, compared
with 28% ten years ago. But S.A.T. verbal scores averaged 12
points lower and math scores 3 points lower than they were ten
years ago. The disparity has led College Board president Donald
Stewart to commission the Rand Corporation to study the trend.
Stewart wants to know if it really represents positive changes in
education. He worries that "it may also reflect greater focus on
personal qualities instead of academic achievement."

Stewart speculates that the apparent grade inflation may be
attributable in part to increased emphasis on teacher
accountability. Teachers who are supposed to be improving may be
covering themselves by giving out higher grades. This would be
exposed by standardized tests. This interpretation was disputed
by Bob Schaeffer of the Fairtest organization, a longtime critic
of the College Board. He argues that high school record is a
better predictor of college performance than the S.A.T.

Beyond the overall average, Stewart noted two other disturbing
trends. First, suburban students are improving their S.A.T.
scores, while urban and rural students are falling behind. There
is now a 30-point gap between urban and suburban students.
Second, the scores for children with less education are falling
further below the national average.

The article is accompanied by a graphic entitled "Keeping Track:
Suspicious Growth of A's" Here are the data:

(1) From the data in the table, how can you see that the
percentage of test-takers with 'A' averages, has grown by 10%?
How do you see that the verbal scores have fallen by 12 points?

(2) What do you think of the Fairtest argument presented in the
article? If college grades are also being inflated, wouldn't you
expect inflated high school grades be a good predictor of first
year college grades?